Tables
How can you use the pattern’s table to find the slope?
 When a table represents a linear pattern, the slope can be found by computing the ratio of the change in \(y\) and the change in \(x\).
 One way to compute the slope in linear tables is to order the \(x\)values so that they increase by equal increments. When arranged in this manner, the change in the \(x\)values and the \(y\)values can be computed and used in the ratio to determine slope.
The computation for the slope for Pattern 1 is shown in the table below where x represents the step and y represents the number of squares in that step. Tables are created using Desmos.com.
\[slope=\frac{\Delta y}{\Delta x} =\frac {rise}{run}=\frac {+2}{+1}=2\]
Another way to compute the slope from a table is to choose any two points and compute the ratio of the change in \(y\) and the change in \(x\) between these two points.

 For example, choosing the points \((1,6)\) and \((4,12)\) from the table above, we can find the change in \(y\) and the change in \(x\):
\[slope=\frac{\Delta y}{\Delta x}=\frac{(126)}{(41)}=\frac {6}{3}=2\]
This method defines the formula for finding slope between any two points on a line where the first point is defined as \((x_1,y_1)\) and the second point is defined as \((x_2,y_2)\): \[slope=\frac{(y_2y_1)}{(x_2x_1)}\]
 Compute the slope for the remaining patterns by ordering the \(x\)values in each table or by choosing two points and using the slope formula.
Check your solutions using the results from the previous page: Making Connections (Graphed Points).